what transformation always results in isometery?
rotation,reflection, and translation
An isometry is a transformation that preserves distances between points in a geometric figure. This means that after applying an isometry, the shape and size of the figure remain the same. There are three main types of isometries:
1. Translation: A translation is a transformation that slides a figure in a certain direction without rotating or reflecting it. This transformation preserves distances and angles, resulting in an isometry. For example, moving an object three units to the right and two units up is a translation.
2. Rotation: A rotation is a transformation that rotates a figure around a fixed point called the center of rotation. The amount of rotation is measured in degrees or radians. If a figure is rotated by any angle, the distances between points remain the same, resulting in an isometry. For example, rotating an object 90 degrees counterclockwise is a rotation isometry.
3. Reflection: A reflection is a transformation that flips a figure across a line called the line of reflection. Points on the original figure and their corresponding points on the reflected figure are equidistant from the line of reflection. This transformation preserves distances and angles, making it an isometry. For example, reflecting an object across a vertical line is a reflection isometry.
It is important to note that a combination of translations, rotations, and reflections can also result in an isometry.
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